A magnetic needle free to rotate in a fixed vertical plane stays in a direction making an angle of `60^@` with the horizontal. If the dip at that plane is `37^@`, find the angle of the fixed vertical plane with the meridian.

Explanation

If the vertical plane makes an angle `theta` with the meridian, the horizontal component of the earth's field in that plane will be `B_H costheta`. Thus the apparent die `delta_1`, i.e., the angle between the needle in equilibrium and the horizontal will be given by
`tandelta_1 = (B_v)/(B_H costheta) = (tandelta)/(costheta)`
or, `costheta = (tandelta)/(tandelta_1)`
`= (tan 37^@)/(tan 60^@ = 3/(4sqrt(3) = (sqrt(3))/(4)`
or, `theta = 64^@`.